I would prefer 3-betting pf unless you have been 3-bet/4-bet history and you don´t really want to get all-in pf with AQ
If you want to c/r for value you should also get all-in that flop, since he can have a lot of draws that he would shove over your c/r and pair+draws, like QJ, maybe 8sxs.
You of course also has option to just c/c and call him down to let him bluff his air. This way you don´t loose your whole stack if you´re behind